Let \(A = \{ x \in W | x < 2\}\), \(B = \{x \in N | 1 < x \le 4\}\) and \(C = \{-5, 3, 8\}\). Verify that \(A \times (B \cap C) = (A \times B) \cap (A \times C)\).
Proof:
\(B \cap C =\)
\(A \times B \cap C =\)
\(A \times B =\)
\(A \times C =\)
\((A \times B) \cap (A \times C) =\)
Thus, \(A \times (B \cap C) = (A \times B) \cap (A \times C)\).
Hence proved.
Answer variants: